Analysis & PDE

  • Anal. PDE
  • Volume 6, Number 4 (2013), 973-991.

Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity

Thierry Gallay and Yasunori Maekawa

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We consider the incompressible Navier–Stokes equations in a two-dimensional exterior domain Ω, with no-slip boundary conditions. Our initial data are of the form u0=αΘ0+v0, where Θ0 is the Oseen vortex with unit circulation at infinity and v0 is a solenoidal perturbation belonging to L2(Ω)2Lq(Ω)2 for some q(1,2). If α is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation α. This is a global stability result, in the sense that the perturbation v0 can be arbitrarily large, and our smallness assumption on the circulation α is independent of the domain Ω.

Article information

Anal. PDE, Volume 6, Number 4 (2013), 973-991.

Received: 28 February 2012
Accepted: 6 August 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B35: Stability 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30] 76D17: Viscous vortex flows

Navier–Stokes equations exterior domains long-time asymptotics Oseen vortices


Gallay, Thierry; Maekawa, Yasunori. Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity. Anal. PDE 6 (2013), no. 4, 973--991. doi:10.2140/apde.2013.6.973.

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